Question

What is the longest-wave lenght line in nm in the infrared seris for hydrogen where m=3? please show work. Thanks

Answer 1

Ans- Rydberg's formula gives the wavelength w for photons emitted or absorbed by electrons jumping between energy levels m and n. If m is the lower energy level the longest wavelength (least energy) would be for a transition between m = 3 and n = 4; that is, for a transition from level 4 to level 3. The formula is: 1/w = R(1/m² - 1/n²) where R is Rydberg's constant, experimentally determined as 10,967,758 waves per meter for hydrogen. Substituting in the given values, we obtain: 1/w = 10967758(1/9 - 1/16) = 10967758(0.111111 - 0.0625) Do the arithmetic and we get 1/w = 10967758(0.0486111) = 533154.78 So if 1/w = 533154.78 waves per meter, w = 1/533154 = 1.875 * 10**-6 meter So the wavelength is 1.875 * 10**-6 meter, or 1.875 microns. This wavelength is in the infrared range.